Problem 22 - Chemistry: An Atoms-Focused Approach

Question

How are the mass number and atomic number of a nuclide related to the number of neutrons and protons in each of its nuclei?

Step-by-Step Solution

Answer

Answer: To determine the number of neutrons (n) and protons (p) in a nuclide's nucleus, you can use the following relationships between mass number (A), atomic number (Z), and the number of neutrons (n) and protons (p): - Protons (p) are equal to the atomic number (Z): p = Z - Neutrons (n) can be calculated as the difference between the mass number (A) and the atomic number (Z): n = A - Z

Step 1: Define mass number and atomic number

Mass number (A) is the total number of protons and neutrons found in the nucleus of an atom. Atomic number (Z) is the number of protons in the nucleus of an atom.

Step 2: Express mass number in terms of protons and neutrons

As mass number (A) is the total number of protons and neutrons, we can express it as the sum of the number of protons (p) and the number of neutrons (n). \[A = p + n\]

Step 3: Relate atomic number to the number of protons

Since atomic number (Z) is the number of protons in the nucleus of an atom, we can define it as: \[Z = p\]

Step 4: Find the relationship between atomic number, mass number, and the number of neutrons

From steps 2 and 3, we know that: \[A = p + n\] and \[Z = p\] Now, we can substitute the second equation into the first equation to find the relationship between atomic number (Z), mass number (A), and the number of neutrons (n). \[A = Z + n\] So, the number of neutrons in a nucleus can be calculated as the difference between the mass number and the atomic number: \[n = A - Z\] In conclusion, the mass number (A) and atomic number (Z) of a nuclide are related to the number of neutrons (n) and protons (p) in its nucleus by the following equations: \[A = p + n\] \[Z = p\] \[n = A - Z\]